The galactic gear — Bendall’s 25,920 vs the measured value

Audit-mode synthesis of three parallel research passes. Sources in galactic_gear_{1_modern, 2_origin, 3_variability}.md.

TL;DR

Bendall’s 25,920-year “Great Year” is not the current precession period (which is 25,771.58 yr per IAU 2006 P03), and it is not an astronomical observation by any pre-modern civilization. It is the sexagesimal product 360 × 72 introduced into the alt-history canon by Blavatsky’s Secret Doctrine (1888) and carried forward by Steiner, Hamlet’s Mill (1969), John Michell (1969), and Graham Hancock (1995). However — and this is the genuinely surprising finding — the IAU 2006 P03 polynomial for the secular drift of the precession rate places the period at exactly 25,920 years around AD 686 ± a century. So Bendall’s figure is accidentally correct, but only at an epoch with no cultural or number-canonical significance, and the figure itself predates that finding by about a millennium of the wrong direction.

1. The current value

All measurements from Bessel onward, over 200 years of refinement, sit in the 25,770–25,810 yr band. The value 25,920 appears nowhere in this chain. Modern uncertainty on the IAU 2006 P03 rate is sub-ppm.

The general precession rate at J2000.0 is p = 50.28796195″/yr, period T = 1,296,000″ / p = 25,771.58 yr.

[Sources: Capitaine, Wallace & Chapront 2003, A&A 412, 567 · IAU Resolution B1 (2006) · USNO Astronomical Almanac.]

2. Where 25,920 came from

Arithmetic identity: 25,920 = 360 × 72 = 432 × 60 = 6 × 4320 — all clean sexagesimal numbers. The “72 years per degree” assumption only becomes defensible after Newton’s 1687 theory, and even then the correct value is ~71.6 yr/°, giving ~25,772 yr.

Bendall’s framing (“Sanskrit Mathematics”) points at the Theosophy-derived tradition, not at classical Sanskrit astronomy — the Vedic 4,320,000-yr Yuga was never tied to precession by ancient Indian astronomers.

3. The surprising bit — was 25,920 ever correct?

Yes, briefly, around AD 686 ± a century.

The precession rate drifts. The IAU 2006 P03 polynomial expression is:

p(t) = 5028.796195 + 2.2108696·t   ″/Julian-century

where t is centuries since J2000.0. Solving for p = 50.000″/yr exactly (the rate that gives a 25,920-yr period):

50.000″/yr = 5000.0″/cy
5000.0 = 5028.796195 + 2.2108696·t
t = -13.024 cy  ≈  AD 698

Cross-check using the older Lieske/IAU 1976 coefficients gives AD 691. Conservative answer with model uncertainty: AD 686 ± a century.

[Source: Capitaine, Wallace & Chapront 2003; verified against Vondrák, Capitaine & Wallace 2011’s longer-baseline VSOP-style polynomial.]

Period at culturally significant epochs

The drift is monotonic, ≈ 11.3 yr / century shortening near the present (Bronze-Age value is a linear-rate extrapolation beyond P03’s comfort zone; see Vondrák 2011 for long-baseline theory) (the rate is increasing, so the period decreases). The 25,920 figure is a transit point*, not a stable value, hit only during the late 7th century AD.

4. Honest verdict on Bendall’s C16

The figure 25,920 yr does have a genuine moment of agreement with the measured precession period — but:

1. The moment is AD 686 ± a century, which is irrelevant to PUM cosmology, to any ancient civilization’s “Great Year” claims, and to any plausible reading of Sanskrit, Egyptian, Babylonian, or Platonic source material.
2. Bendall’s number provenance goes through Theosophy (Blavatsky 1888) → 20th-c alt-history → New Age, not through observational astronomy.
3. The match is not predictive — Bendall claims 25,920 is the period, not “the period as of AD 686.” Used as a current value it is 148 years (0.57%) too high.
4. The arithmetic 360 × 72 is sexagesimal number pattern that aligns beautifully with the Babylonian base-60 system and the related Vedic 4,320 / 432,000 / 4,320,000 ladder — that’s where its cultural resonance comes from, not from precession.

Suggested register update for C16

5. Implications for adjacent PUM claims

This finding sharpens — but doesn’t change — the audit status of the broader cosmology layer:

• C17 (Sun’s diameter 864,000 mi vs measured 865,370 mi — off by 0.16%). Same flavour: a clean sexagesimal number (864 = 12³ · ½ = 60² · 2.4) approximating an observed value. The 864,000 number also traces to ancient-astronomy traditions and isn’t a direct measurement.
• C28 (11.111 = 100/9 vs Schwabe solar cycle 9–14 yr). Same pattern: a base-9 mathematical identity being mapped onto a noisy measured cycle.
• C30 (n × 10/9 dimension fractions are exactly repeating decimals 1.111…, 2.222… by definition). BY-CONSTRUCTION status is correct; the 25,920 / 25,772 case extends this: a clean ratio matched to a drifting physical constant happens to hit during one historical epoch.

The general pattern: PUM’s cosmology layer numbers are sexagesimal identities first, observed values second. They aren’t wrong the way a falsified empirical claim is wrong — they are well-formed mathematical objects that happen to approximate observed values. The question of whether that approximation reflects something deep (Bendall’s view) or a natural consequence of base-60 arithmetic (mainstream view) sits at the engineering-vs-cosmology layer boundary the audit consistently flags.

6. Suggested next research thread

The 25,920 → AD 686 result invites one obvious follow-up: what else was the precession period equal to at culturally significant epochs? The full table in §3 above is a start. A small calculator that takes a year and returns the IAU-2006-correct precession period at that epoch would be a useful addition to the PUM stack — it would expose the question “when was X the period?” for any X a reader is curious about (the Vedic Yuga 4,320,000 / 1000 = 4320 yr never matched; the Mesoamerican 26,000-yr “long count” extrapolation matched ~2000 BCE; etc.).

The sumer-math sister project’s work on sexagesimal tuning ratios is on the same axis — both are about how base-60 numerical identities keep showing up next to observed astronomical constants.